Method and system to separate optically measured coupled parameters

ABSTRACT

A system includes a first optical sensor sensitive to both a parameter of interest, Parameter1, and at least one confounding parameter, Parameter2 and a second optical sensor sensitive only to the confounding parameter. Measurement circuitry measures M 1  in response to light scattered by the first optical sensor, where M 1 =value of Parameter1+K*value of Parameter2. The measurement circuitry also measures M 2  in response to light scattered by the second optical sensor, where M 2 =value of Parameter2. Compensation circuitry determines a compensation factor, K, for the confounding parameter based on measurements of M 1  and M 2  taken over multiple load/unload cycles or over one or more thermal cycles. The compensation factor is used to determine the parameter of interest.

RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.14/810,919, filed Jul. 28, 2015, to which priority is claimed pursuantto 35 U.S.C. § 119(e), and which is incorporated herein by reference inits entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

This invention was made with government support under contractDE-AR0000274 awarded by ARPA-E (Advanced Research ProjectsAgency—Energy). The government has certain rights in the invention.

TECHNICAL FIELD

This disclosure relates generally to systems that use optical sensorsthat provide coupled parameter measurements and to related methods anddevices.

BACKGROUND

Optical sensors such as fiber Bragg grating (FBG) sensors offer a lowcost, compact, and robust sensing mechanism for measurement of a varietyof quantities such as strain, temperature, chemical composition,electric current, etc. In many cases, the sensing environment presentschanges in more than one quantity at the same time. For example, in somescenarios, thermal changes occur together with structural changes (e.g.,as measured by strain). Alternatively or additionally, chemical changesmight happen at the same time as thermal changes. Thus, measurementsobtained from optical sensors can be a combination of changes in one ormore quantities.

BRIEF SUMMARY

Some embodiments are directed to a system that includes one or morefiber optic cables arranged within or on portions of a battery. At leastone fiber optic cable includes at least a first optical sensor sensitiveto both a parameter of interest, Parameter1, and a confoundingparameter, Parameter2. At least one fiber optic cable includes a secondoptical sensor sensitive only to the confounding parameter. The systemincludes measurement circuitry is configured to measure M₁ in responseto light scattered by the first optical sensor, where M₁=value ofParameter1+K*value of Parameter2. The measurement circuitry is alsoconfigured to measure M₂ in response to light scattered by the secondoptical sensor, where M₂=value of Parameter2. The system includescompensation circuitry configured to determine a compensation factor, K,for the confounding parameter based on measurements of M₁ and M₂ takenover multiple charge/discharge cycles or over one or more thermal cyclesof the battery.

Some embodiments involve a method for determining a compensation factorfor decoupling coupled parameters sensed using optical sensors. Lightscattered by a first optical sensor on or within a battery is sensed andlight scattered by a second optical sensor disposed one or within thebattery is sensed. The battery is subjected to charge/discharge cyclingor thermal cycling. During the cycling, M₁ is measured in response tolight scattered by the first optical sensor and M₂ is measured inresponse to light scattered by the second optical sensor, where M₁=valueof Parameter1+K*value of Parameter2 and M₂=value of Parameter 2.Parameter1 is a parameter of interest and Parameter2 is a confoundingparameter. A compensation factor, K, for the confounding parameter isdetermined based on the measurements of M₁ and M₂ during the cycling.

According to some embodiments, one or more fiber optic cables arearranged within or on a mechanical structure. At least one fiber opticcable includes at least a first optical sensor sensitive to both aparameter of interest, Parameter1, and a confounding parameter,Parameter2. At least one fiber optic cable includes a second opticalsensor sensitive only to the confounding parameter. Measurementcircuitry is configured to measure M₁ in response to light scattered bythe first optical sensor, where M₁=a value of Parameter1 plus K*a valueof Parameter2. The measurement circuitry is configured to measure M₂ inresponse to light scattered by the second optical sensor, where M₂=avalue of Parameter2.

Compensation circuitry is configured to determine a compensation factor,K, for the confounding parameter based on measurements of M₁ and M₂taken over multiple load/unload cycles or over one or more thermalcycles of the structure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a system configured to measure outputs M₁and M₂ from two optical sensors disposed in or on a battery and todetermine the compensation factor K for the coupled measurement M₁ inaccordance with some embodiments;

FIG. 2 is block diagram of a management system for a mechanicalstructure;

FIG. 3 is a flow diagram illustrating a process for determining anoptimal compensation factor in accordance with some embodiments whereinthe process may be implemented by the systems illustrated in FIG. 1 or2;

FIG. 4A is a flow diagram that illustrates in more detail an approachfor determining the compensation factor of a battery or other mechanicalstructure based on multiple load/unload cycles of the structure inaccordance with various embodiments;

FIGS. 4B and 4C are graphs that illustrate in more detail the processfor determining K outlined by the flow diagram of FIG. 4A;

FIG. 5A is a flow diagram that illustrates in more detail an approachfor determining the compensation factor for a battery based on thermalcycling in accordance with some embodiments;

FIG. 5B is a flow diagram that illustrates in more detail an approachfor determining multiple compensation factors for multiple confoundingparameters based on measurements taken over one or more cycles that spana range of values of each of the confounding parameters;

FIGS. 6A and 6B are graphs that show the value of the objective functionas a function of the compensation factor, K, for a first experimentbased on charge/discharge cycling;

FIGS. 7A and 7B are graphs that show the value of the objective functionas a function of the compensation factor, K, for a second experimentbased on charge/discharge cycling; and

FIGS. 8A and 8B are graphs that show the optimal compensation factordetermined by the thermal cycling;

FIG. 9 depicts a physical or cyber physical system that includes one ormore measureable inputs 901 and n outputs for which one or morecompensation factors can be determined; and

FIG. 10 is a graph illustrating the invariancy of the parameter ofinterest with respect to Q, where Q is a function of the measurableinput, e.g., current.

The figures are not necessarily to scale. Like numbers used in thefigures refer to like components. However, it will be understood thatthe use of a number to refer to a component in a given figure is notintended to limit the component in another figure labeled with the samenumber.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Embodiments described herein relate to systems and methods to separatemeasurements of coupled parameters sensed by optical sensors intoconstituent decoupled values and to use the decoupled values todetermine the state of health and/or to manage mechanical structures.

As an example, consider a lithium ion battery as a mechanical structure.Lithium-ion batteries have grown increasingly popular in recent yearswith widespread use in consumer electronics and electric vehicles. Morerecently, they have also been used in commercial aircraft. Lithium ionbatteries, however, are used conservatively. In other words, theircapacities remain underutilized, and their operating voltage and currentlimits are also set conservatively. This is because lithium ionbatteries can degrade if not operated within their performance limits,and can sometimes fail catastrophically leading to potential safetyissues in their environment of operation. Measurement of externalbattery parameters such as voltage and current may not provide accurateinformation about the state of health of the battery. Strainmeasurements, e.g., taken internally within the battery, potentiallyprovide richer information about the battery state. Fiber optic sensors(e.g., FBG sensors) are one of the most effective sensors to measurestrain. However measurement of strain using a FBG sensor is complicatedby concurrent changes in the FBG sensor output due to changes in otherparameters, such as temperature. Thus, for some measurements, strain andtemperature are coupled parameters, where strain is the parameter ofinterest and temperature is a confounding parameter. Alternatively, insome measurements temperature is the parameter of interest with strainbeing the confounding parameter. Strain and current, temperature andcurrent, temperature and chemical composition, strain and chemicalcomposition are additional examples of coupled parameters, where thefirst parameter listed is the parameter of interest and the secondparameter is a confounding parameter.

The problem of coupled parameters when using optical sensors extendsbeyond lithium ion batters or batteries in general to physical systems,and/or cyber physical systems. For example, strain and temperature arecoupled parameters for a variety of mechanical structures, e.g., loadbearing support structures such as bridge supports, trusses, aircraftwings, etc. Although the examples provided below refer to a battery asthe system from which measurements are taken and the compensationfactors are determined, it will be appreciated that the conceptsdisclosed herein are also applicable to other systems.

Assume that a parameter M₁ can be measured using an optical sensor,wherein M₁ is a combination of two parameters, one parameter(Parameter1) being the parameter of interest and at least one otherparameter (Parameter2) being a parameter that confounds the measurementof the first parameter and is referred to herein as the confoundingparameter. The quantity measured from the FBG sensor is: M₁=value ofParameter1+K*value of Parameter2, where K is an unknown compensationfactor.

Embodiments disclosed herein describe methods and systems to determinethe value of K and to recover the values of Parameter 1 and Parameter 2.Without loss of generality to other subsystems, some embodiments of thisdisclosure describe systems and methods for determining values K,Parameter 1, and/or Parameter2 using the example of strain andtemperature within the context of lithium ion batteries. The examplesprovided illustrate systems and methods for determining a compensationfactor for the coupled measurement wherein there is one confoundingparameter. It will be appreciated that there may be multiple confoundingparameters for each parameter of interest. The methods and systemsdiscussed below are also applicable to the determination of compensationfactors K₂, K₃, K₄, . . . K_(N) for multiple confounding parameters,Parameter2, Parameter3, Parameter4, . . . , ParameterN, where M₁=valueof Parameter1+K₂*Parameter2+K₃*Parameter3+K₄*Parameter4+ . . .K_(N)*ParameterN. In a scenario where multiple confounding parametersfor a parameter of interest, Parameter1, are present, the systemincludes multiple sensors, sensor2, sensor3, . . . sensorN sensitive,respectively, only to Parameter2, Paramter3, . . . ParameterN.

Measurements of strain in a lithium ion battery can be obtained bybonding FBG sensors to a battery cell, e.g., either bonded externally tothe battery cell skin or bonded internally to the battery. In thisconfiguration, a measurement M₁ obtained from a first sensor is a linearcombination of strain and temperature, where strain is a parameter ofinterest and temperature is a confounding parameter,M₁=Strain+K*Temperature.

It is possible to attach a second sensor in such a way such that onlythe temperature can be measured, e.g., by placing the second sensorloosely in the battery in a way that it is not affected or is minimallyaffected by strain. In this scenario, the second sensor provides asecond measurement, M₂ Temperature.

Using measurements M₁ and M₂, strain can be determined if thetemperature compensation factor K is known. Embodiments disclosed hereinprovide systems and methods for determining K, for determining the stateof health of mechanical structures and/or for managing mechanicalstructures based on the determination of K.

FIG. 1 is a block diagram of a system 100 configured to measure outputsM₁ and M₂ from two optical sensors disposed in or on a battery 110 andto determine the compensation factor K for the coupled measurement M₁.System 100 includes sensors 121, 122 disposed in, on, or about thebattery 110, wherein FBG sensor 121 is arranged so that FBG sensor 121is affected by both strain and temperature and FBG sensor 122 isarranged so that FBG sensor 122 is affected by temperature and is notaffected or is minimally affected by strain. Although the sensors 121,122 are shown disposed on two separate waveguides, the sensors mayalternatively be disposed on a single waveguide wherein the outputs ofthe sensors are separately discernable, e.g., multiplexed.

FBG sensor 121 and FBG sensor 122 are optically coupled to measurementcircuitry 160 by optical fiber 131 and optical fiber 132, respectively.Measurement circuitry includes a light source 161 configured to provideexcitation light 141, 142 to the FBG sensors 121, 122 through opticalfibers 131, 132. A portion of the excitation light 141, 142 is scatteredby the FBG sensors 121, 122. The wavelengths of the portion 151 ofexcitation light scattered by FBG sensor 121 is dependent on strain andtemperature. The wavelengths of the portion 152 of excitation lightscattered by FBG sensor 122 is dependent on temperature. The measurementcircuitry 160 includes photodetector circuitry 162 comprising one ormore photodetectors configured to detect the wavelengths of thescattered light 151, 152. The measurement circuitry 160 detects shiftsin the wavelengths of the scattered light 151, 152 as the measurementsM₁ and M₂. The measurement circuitry 160 provides an electrical outputthat includes measurements M₁ and M₂.

The measurement circuitry 160 is electrically coupled to compensationcircuitry 170 and the electrical output signal from the measurementcircuitry 160 provides the measurements M₁ and M₂ to the compensationcircuitry 170 for analysis. The compensation circuitry 170, which may beimplemented as a processor or microprocessor, for example, determines acompensation factor K, e.g., an optimal compensation factor (K_(opt)) asdetermined according to the exemplary processes disclosed in more detailbelow. The compensation circuitry can use the optimal value of K and M₂to determine strain from the measurement M₁.

FIG. 2 is a block diagram of a system 200 that includes some of thefeatures of the system of FIG. 1, along with additional optionalfeatures for monitoring and/or management of the battery (or othermechanical structure). The compensation circuitry 170 provides an outputthat includes the temperature and/or strain measurements to a managementprocessor 220. The management processor 220 uses these measurements andoptionally other measurements to control the operation and environmentof the battery using the charge/discharge control circuitry 230 and/orthe environmental control circuitry 240. Collectively the FBG sensors121, 122, the fiber optic cables 131, 132, detection circuitry 160,compensation circuitry 170, management processor 220, internalcharge/discharge control circuitry 230, and external environmentalcontrol circuitry 240 are components of a battery management system 210.

The management system 210 operates to monitor the state of charge of thebattery, the state of health of the battery, e.g., monitoring using themeasured strain and temperature values and/or other parameter values,e.g., external parameters such as voltage and current, controlling thecharging/recharging of the battery and/or controlling the environment ofthe battery so that the battery remains within its safe operating area.

According to various implementations, some aspects charging/dischargingof the battery may be controlled by the management processor 220 andcharge/discharge circuitry 230. For example, these components maycontrol the charge/discharge rate and/or charge/discharge cycles of thebattery. The management processor 220 may use information from theoptical sensors and/or other information to make predictions and/orestimations regarding the state of the battery. These predictions andestimations may be developed using theoretical and/or empirical data andmay be adaptable based on one or more of 1) measured internal orexternal parameters of the battery, e.g., strain, temperature, chemicalcomposition, voltage, current, 2) operational state of the battery,e.g., state of charge/discharge, state of health, 3) external(environmental) parameters and/or 4) correlations between measuredand/or environmental parameters and operational state.

In some cases, information based on measurement and/or analysis ofvarious aspects of battery operation, e.g., the aspects including themeasured internal or external parameters of the battery, operationalstate of the battery, external (environmental) parameters and/orcorrelations between measured and/or environmental parameters andoperational state of the battery can be developed by the managementprocessor 220 and provided to an operator via an electronic or printedreport, e.g. over an external communication link 250. For example, themanagement processor 220 may compile, analyze, trend, and/or summarizethe aspects, and/or may perform other processes based on various aspectsof battery operation. In some configurations, the processes performed bythe management processor include predicting and/or estimating the stateof health of the battery, for example. The results of these processesand/or other information derived from monitoring the battery may beprovided in a report that can be displayed graphically or textually orin any convenient form to a system operator and/or may be provided toanother computer system for storage in a database and/or furtheranalysis.

As a part of the analysis, measurements of strain may be used to monitorthe state of health of a battery (or other mechanical structure).However, as discussed above, when strain values are measured usingoptical sensors such as FBG sensors, the measurement of strain may beconfounded by a concurrent response of the FBG sensor to anotherparameter, such as temperature. Embodiments disclosed herein providesystems and methods for separating coupled parameters measured by FBGsensors by determining a compensation factor.

FIG. 3 is a flow diagram illustrating an approach for determining thecompensation factor based on thermal cycling 312 and/or on multipleload/unload cycles 311. In the case of a battery, charge/dischargecycles provide the load/unload cycles used to determine the compensationfactor. Determining the compensation factor using the load/unloadapproach can be useful in situations where thermal cycling is notpossible or not desirable.

Returning now to FIG. 3, light from the first and second FBG sensors isdetected 320 and first and second electrical signals are generated inresponse to the detected light. The measured values M₁ and M₂ can beextracted 330, 340 from the first and second electrical signals,respectively. The values of M₁ are measurements of a combination of aparameter of interest (e.g., strain) and a confounding parameter (e.g.,temperature, which may also happen to be a parameter of interest). Thevalues of M₂ are measurements of the confounding parameter.

Values of M₁ and M₂ are measured over one or more thermal cycles 312 orover multiple load/unload cycles 311. The compensation factor K isdetermined 350 based on the measured values of M₁ and M₂.

The flow diagram of FIG. 4A illustrates in more detail an approach fordetermining the compensation factor of a battery or other mechanicalstructure based on multiple load/unload cycles of the structure. Theflow diagram of FIG. 4A illustrates an example implementation of element350 of FIG. 3 wherein the mechanical structure is a battery and theload/unload cycles are charge/discharge cycles of the battery.

For each charge/discharge cycle j=1 to N, multiple measurements 410 ofthe charge current, I, M₁, and M₂ are made, e.g. under conditions ofconstant charge and discharge currents. Let I^(j)(t), M₁ ^(j)(t) and M₂^(j)(t) denote the measurements 410 for the jth cycle where t denotesthe time of the measurement. Let [0.01 0.02 . . . 1] be a discretizationof the interval [0,1]. Let p_(i) denote the ith point in the interval.Therefore, p₁=0.01, p₂=0.02, and so on. For each cycle j, the state ofcharge 420, SOC^(j)(t)=Σ_(i=0) ^(t)I^(j)(i)ΔT is computed where ΔT isthe time difference between successive measurements. For each cycle, j,and each time index, i, r=argmin_(t)|SOC^(j)(t)−p_(i)| is determined430. For this determination, r is the time instant, t, wherein theabsolute value of the difference between the state of charge (SOC) andthe discretization point is minimized. Thus, for the first time indexi=1, discretization point p₁ is 0.01, and r is the time at which thestate of charge (SOC) of the battery is at 1%; for the second timeindex, discretization point p₂ is 0.02, and r is the time at which theSOC is of the battery is 2%, etc. For each r, determine 440 M₁ ^(j)(r)and M₂ ^(j)(r). For each cycle, j, and each index, i, determine 450M(K,j,i)=M₁ ^(j)(r)−KM₂ ^(j)(r). Compute the standard deviation 460 ofM(K,j,i) over all cycles j at each point, p_(i). To compute the standarddeviation, first the mean μ(K,i)=1/NΣ_(j=1) ^(N)M(K,j,i) is determined.Then, the standard deviation can be determined

${{\sigma \left( {K,\ i} \right)} = \sqrt{\left( {\frac{1}{N}{\sum_{j = 1}^{N}\left( {{M\left( {K,j,i} \right)} - {\mu \left( {K,i} \right)}} \right)^{2}}} \right.}}.$

Define an objective function which sums 470 the standard deviations of Kover each value of i, J(K)=Σ_(i)σ(K,i). Determine 480 the K thatminimizes the sum of the standard deviations, K_(opt)=argmin_(K)J(K).

In some embodiments, K_(opt) can be determined numerically by evaluatingthe objective function at different possible values of K. K_(opt) isthen set to be the value of K for which J is the least. Without loss ofgenerality K can represent a vector of parameters (K2, . . . , KN). Inthis case, to find the optimal vector K_(opt), we can evaluate J fordifferent combinations of (K2, . . . , KN) and then set K_(opt) to thebe combination for which J is the least.

In an alternate process, determine 490 K that minimizes the maximumstandard deviation of the standard deviations at the points p_(i). Thestrain in the battery is determined using the measurements M₁, M₂, andK_(opt).

Some embodiments rely on determining residual strain during the periodswhen the battery is at rest (not being charged or discharged) and/or hasbeen at rest for a specified sufficient amount of time. In other words,r=argmin_(t)|SOC^(j)(t)−p_(i)| is computed for those time instants whenthe cell is completely at rest and has been at rest for a specifiedamount of time.

In the process outlined by the flow diagram of FIG. 4A, it will beappreciated σ(K,i) may be non-zero because the current I^(j)(t) differsfrom one cycle to the next resulting in different temperature profilesover the course of multiple charge and discharge cycles. Alternativelyor additionally, natural variations in experimental conditions may occurfrom cycle to cycle even though I^(j)(t) is substantially identical foreach cycle. In some embodiments, some minor controlled temperaturefluctuations may be introduced during the charge and discharge cycles.These controlled temperature fluctuations cause σ(K,i) to be non-zeroand may facilitate obtaining Kor.

FIGS. 4B and 4C are graphs that illustrate in more detail the processfor determining K outlined by the flow diagram of FIG. 4A. FIGS. 4B and4C each show a family of traces of M(K)=M₁−KM₂ vs. SOC at discretizationindex points p_(i), where M₁ and M₂ are measured from multiple cycles,j=1, . . . N. The family of traces shown in FIG. 4B have a relativelyhigher objective function, J(K) (sum of the standard deviations of thetraces at the index points) when compared to the family of traces shownin FIG. 4C.

FIG. 4B shows traces 401-404 corresponding to M(K,j,i) vs. SOC at indexpoints p_(i), which are the discretization points of SOC forcharge/discharge cycles 1, 2, j, and N, respectively. Trace 401corresponds to M(K,1,i) for the first cycle j=1; trace 402 correspondsto M(K,2,i) for the second cycle; trace 403 corresponds to M(K,j,i) forthe jth cycle; and trace 404 corresponds to M(K,N,i) for the Nth cycle.Points M(K,1,2), M(K,2,2), M(K,j,2), M(K,N,2) indicate points for thefirst, second, jth, and Nth cycles for discretization point p2=0.02.These points correspond to the value of M=M₁−K*M₂ at which the SOC isclosest to 2% for each cycle. Points M(K,1,99), M(K,2,99), M(K,j,99),M(K,N,99) indicate points for the first, second, jth, and Nth cycles fordiscretization point p₉9=0.99. These points correspond to the value ofM=M₁−K*M₂ at which the SOC was closest to 99% for each cycle. Thestandard deviations for M(K,j,i) are determined at each discretizationpoint, p_(i), over all cycles j=1 to N. Thus, the standard deviation ofthe group of points 411 at p₂ is determined, the standard deviation ofthe group of points 412 at p₉₉ is determined along with the standarddeviations at some or all of the other discretization points p₁, p₃-p₉₈,and p₁₀₀ (not specifically indicated in FIG. 4B). The objective junctionJ(K) is the sum of the standard deviations for each discretizationpoint, J(K)=Σ_(i)σ(K,i)=σ(K,1)+σ(K,2)+σ(K,3)+ . . . .σ(K,99). Theminimum of J(K) corresponds to the situation wherein the traces forM(K,j,i) lie nearly on top of one another and provides an optimal valueof K. FIG. 4B shows the family of traces 401-404 (corresponding tocycles 1, 2, j, N) with a suboptimal K wherein the objective functionJ(K) is not minimized. FIG. 4C illustrates the family of traces 401-404with optimal K=K_(opt) wherein the objective function J(K) is minimized.

The flow diagram of FIG. 5 illustrates in more detail an approach fordetermining the compensation factor of a battery based on thermalcycling. The flow diagram of FIG. 5 illustrates an exampleimplementation of element 312 of FIG. 3 wherein strain is the parameterof interest, temperature is the confounding parameter.

The compensation factor, K, can be determined empirically by heating thebattery at rest (not being charged or discharged) to varioustemperatures and measuring 510 M₁ and M₂. Because the cell is at rest,M₁=K*Temperature. The temperature compensation factor, K, is determined510 based on a ratio of M₁ and M₂, e.g.,

${K = \frac{M_{1}}{M_{2}}}.$

The flow diagram of FIG. 5B illustrates an example implementation ofelement 312 of FIG. 3 wherein strain is the parameter of interest,temperature is a confounding Parameter2, and humidity is confoundingParameter3. In this example, the subsystem under test is a mechanicalstructure. M₁ is measured using the output of a first optical sensorwhich is sensitive to the parameter of interest (strain) and theconfounding parameters temperatures and vibration, where M₁=value ofParameter 1+K₂*value of Parameter2+K₃*value of Parameter3, orM₁=Strain+K₂*Temperature+K₃*humidity. Measurement M₂ can be obtainedfrom an optical sensor which is sensitive only to temperature andmeasurement M₃ can be obtained from an optical sensor which is sensitiveonly to humidity, M₂ Temperature and M₃ Humidity.

The compensation factor, K₂ for confounding Parameter2 (temperature),can be determined empirically by heating the mechanical structure atrest not being loaded and experiencing no humidity to varioustemperatures, for example inside an environmental chamber, and measuringM₁ and M₂. Because the mechanical structure is at rest,M₁=K₂*Temperature. The temperature compensation factor, K₂, isdetermined based on a ratio of M₁ and M₂, e.g.,

${K_{2} = \frac{M_{1}}{M_{2}}}.$

The compensation factor, K₃ for confounding Parameter3 (humidity), canbe determined empirically subjecting the mechanical structure at restnot being loaded and at a known constant temperature to differentamounts of humidity and measuring M₁ and M₃. Because the mechanicalstructure is at rest, M₁=K₂*Temperature+K₃*Humidity. The humiditycompensation factor, K₃, is determined based on a ratio ofM₁−K₂*temperature and M₃, e.g.,

${K_{3} = {\frac{M_{1} - {{K2}*{Temperature}}}{M_{3}}\mspace{14mu} {or}}}\mspace{14mu}$$K_{3} = {{\frac{M_{1} - {K2*M_{2}}}{M_{3}}\mspace{14mu} {since}\mspace{14mu} M_{2}} = {{Temperautre}.}}$

More generally M₂ and M₃ could measure known combinations of temperatureand humidity. For example, M₂=α*Temperature+β*Humidity andM₃=γ*Temperature+δ*Humidity where α, β, γ, δ are known and chosen insuch a way that

$\begin{bmatrix}\alpha & \beta \\\gamma & \delta\end{bmatrix}$

is invertible. Therefore, we have

${Temperature} = {\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{\delta M_{2}} - {\beta M_{3}}} \right)}$${Humidity} = {\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{{- \gamma}M_{2}} + {\alpha M_{3}}} \right)}$

Therefore, we can write

$M_{1} = {{strain} + {K_{2}*\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{\delta M_{2}} - {\beta M_{3}}} \right)} + {K_{3}*\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{{- \gamma}M_{2}} + {\alpha M_{3}}} \right)}}$

The parameters K₂ and K₃ can be determined by subjecting the mechanicalstructure to two different combinations, C1 and C2, of temperature andhumidity, under no loading (strain=0), and measuring M1, M2, and M3 550,560. Then K2 and K3 can be determined 570 as follows

$\begin{bmatrix}K_{2} \\K_{3}\end{bmatrix} = {\begin{bmatrix}{\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{\delta {M_{2}\left( {C1} \right)}} - {\beta {M_{3}\left( {C1} \right)}}} \right)} & {\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{{- \gamma}{M_{2}\left( {C1} \right)}} + {\alpha {M_{3}\left( {C1} \right)}}} \right)} \\{\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{\delta {M_{2}\left( {C2} \right)}} - {\beta {M_{3}\left( {C2} \right)}}} \right)} & {\frac{1}{{\alpha \delta} - {\gamma \beta}}\left( {{{- \gamma}{M_{2}\left( {C2} \right)}} + {\alpha {M_{3}\left( {C2} \right)}}} \right)}\end{bmatrix}^{- 1}{\quad\begin{bmatrix}{M_{1}\left( {C1} \right)} \\{M_{1}\left( {C2} \right)}\end{bmatrix}}}$

where Mi(C1) and Mi(C2) denote the measurements Mi at combination 1 oftemperature and humidity and combination 2 of temperature and humidity,respectively. The right hand side of the above expression can be thoughtof as a generalized ratio of M1 and M2, M3.

The thermal cycling and/or charge/discharge methods described above maybe used, for example, during the formation stage of the battery in whichthe battery is subjected to charge and discharge cycles in order toslowly form the solid-electrolyte interphase.

EXAMPLES

Two sets of charge and discharge experiments (referred to as Experiment1 and Experiment 2) were performed and the optimal temperaturecompensation factors were determined according to the charge/dischargemethod described above with reference to FIGS. 4A through 4C. InExperiments 1 and 2, the optimal compensation factor K determined was4.1 and 3.7, respectively, for the battery tested. FIGS. 6A and 6B showthe value of the objective function as a function of the compensationfactor, K, for Experiment 1. FIG. 6B is a zoomed inversion of FIG. 6A atthe optimal compensation factor 610. FIGS. 7A and 7B show the value ofthe objective function as a function of the compensation factor K forExperiment 2. FIG. 7B is a zoomed in version of FIG. 7A at the optimalcompensation factor 710.

Additionally, the compensation factor for the battery was determinedusing the thermal cycling process described above with reference to FIG.5. As shown in FIGS. 8A and 8B, the optimal compensation factordetermined by the thermal cycling method was 3.88. FIG. 8A shows theratio of M₁ to M₂ along the y axis with respect to measurement points.FIG. 8B shows traces for M₁ 810 and M₂ 820. In steady state (relativelyconstant M₁/M₂) between points 70000 and 80000 which represent differentpoints in time the ratio of M₁ to M₂ is approximately 3.88. Thedifference between the two approaches (charge/discharge cycling vs.thermal cycling) is less than 6%.

Approaches disclosed herein provide systems and methods for determiningthe optimal compensation factor, for decoupling coupled parameters, andfor using the de-coupled parameters to monitor and/or manage theoperation of a mechanical structure. Where load/unload cycling is usedto determine the optimal compensation factor, there is no need toconduct thermal experiments on the mechanical structure being tested.The compensation factor obtained by these approaches may be optimal forthe unique characteristics of the particular mechanical structure, e.g.,battery cell, and/or the installation configuration. Once initiallydetermined, the optimal compensation factor may be periodicallyre-determined to adjust for changes in the mechanical structure.Additionally, changes in the optimal compensation factor can be used asa measure or indication of degradation of the mechanical structure.Thus, periodic determination of the optimal compensation factor mightprovide indication of degradation the battery or other mechanicalstructure.

According to some embodiments, the compensation factor for a battery canbe determined using the thermal cycling approach based on controlledthermal experiments, for example during formation process in order toslowly build up the solid electrolyte interphase (SEI) at theelectrodes. Additionally or alternatively, the charge/dischargetechnique may be employed for determination of the optimal compensationfactor during battery cell formation.

Some embodiments involve systems and methods that determine thecompensation factor using standard charge and discharge cyclesleveraging the variation in experimental conditions from cycle to cycleand/or by adding some controlled/defined temperature fluctuations.

Approaches disclosed above have been explained with reference tolithium-ion batteries as the mechanical structure for which an optimalcompensation factor for separating coupled parameters strain andtemperature is determined. The approaches are applicable to a variety ofsystems undergoing loading accompanied by thermal changes, or wherethermal changes lead to structural changes. The approaches discussedherein may be used to determine compensation factors that separatevarious overlapping parameters other than strain and temperature thatcan be detected using optical sensors, such as chemical concentration,current, and voltage.

FIG. 9 depicts a physical or cyber physical system 900, wherein aphysical system involves physical processes and a cyber physical systemintegrates physical processes with computation and/or networking. Insome implementations of a cyber physical system, embedded computers andnetworks monitor parameters of the physical processes using sensors andthe embedded computers and networks control the operation of the cyberphysical system using feedback signals that are based on the sensedparameters.

The system 900 includes one or more measureable inputs 901 and n outputsM1 . . . Mn 902. For this system, there exists a quantity Q which is aknown function of the inputs to the system. Furthermore, there exists aparameter of interest Parameter 1 which as a function of Q is invariantunder different inputs. In the case of a battery, a measureable inputmay be current, for example, Q may be state of charge of the battery,and a parameter of interest may be strain. In the case of a physicalsystem, e.g., a bridge, the measureable inputs may be force applied tothe bridge, for example, Q may be the state of loading of the bridge,and a parameter of interest may be strain. In the case of a cyberphysical system, such as a computer controlled machining system, themeasureable inputs may be spindle strain/acceleration, temperature andcutting fluid pH, for example, Q may be the spindle speed and theparameter of interest may be spindle rotor imbalance.

FIG. 10 is a graph illustrating the invariancy of the parameter ofinterest, e.g., strain, with respect to Q, e.g., state of charge, whereQ is a function of the measurable input, e.g., current. The parameter ofinterest is invariant as a function of Q under changes of theexperimental conditions. The condition of invariancy of the parameter ofinterest as a function of Q allows a compensation factor for one or moreparameters that confound the measurement of the parameter or interest tobe determined. A first optical sensor that is sensitive to a parameterof interest (Parameter 1), such as strain, temperature, chemicalcomposition, vibration, or acceleration and to one or more confoundingparameters (Parameter2 . . . ParameterN), such as strain, temperature,chemical composition, vibration or acceleration, is disposed within oron the physical or cyber-physical system. In one example, strain may bea parameter of interest and temperature is a confounding parameter forstrain. As another example, vibration at a particular frequency is aparameter of interest, and dynamic, higher frequency vibration may be aconfounding parameter. Second, third, . . . . Nth optical sensors thatare sensitive only to the confounding parameters Parameter2, Parameter3,. . . ParameterN, respectively, are disposed within or on the physicalor cyber-physical system. Measurement circuitry measures M1 in responseto light scattered by the first optical sensor where M₁=value ofParameter1+g(value of Parameter2, value of Parameter3, . . . value ofParameterN, K₁, K₂ . . . K_(M)) where g is a known function and K₁, K₂,. . . K_(M) are unknown parameters. The measurement circuitry measuresM_(j)=a value of parameter j in response to light scattered by the jthoptical sensor, wherein j is greater than or equal to 2. Thecompensation circuitry determines compensation factors, K₁, K₂ . . .K_(M) for the confounding parameters based on measurements of M₁, M₂, .. . M_(N) taken over multiple load/unload cycles or taken over multiplemeasurable sequences of inputs to the subsystem that result in differentmeasurement sequences of M₁, M₂, . . . M_(N).

Unless otherwise indicated, all numbers expressing feature sizes,amounts, and physical properties used in the specification and claimsare to be understood as being modified in all instances by the term“about.” Accordingly, unless indicated to the contrary, the numericalparameters set forth in the foregoing specification and attached claimsare approximations that can vary depending upon the desired propertiessought to be obtained by those skilled in the art utilizing theteachings disclosed herein. The use of numerical ranges by endpointsincludes all numbers within that range (e.g. 1 to 5 includes 1, 1.5, 2,2.75, 3, 3.80, 4, and 5) and any range within that range.

Various modifications and alterations of the embodiments discussed abovewill be apparent to those skilled in the art, and it should beunderstood that this disclosure is not limited to the illustrativeembodiments set forth herein. The reader should assume that features ofone disclosed embodiment can also be applied to all other disclosedembodiments unless otherwise indicated. It should also be understoodthat all U.S. patents, patent applications, patent applicationpublications, and other patent and non-patent documents referred toherein are incorporated by reference, to the extent they do notcontradict the foregoing disclosure.

1. A method, comprising: sensing light scattered by a first opticalsensor disposed on or within a battery; sensing light scattered by oneor more second optical sensors disposed on or within the battery;charge/discharge cycling or thermal cycling the battery; during thecycling: measuring M₁ in response to sensing light scattered by thefirst optical sensor, where M₁=a value of Parameter1+K*a value ofParameter2 and Parameter1 is a parameter of interest and Parameter 2 isa confounding parameter; and measuring M₂ in response to sensing lightscattered by one of the second optical sensors, where M₂=a value ofParameter 2; and determining a compensation factor, K, for theconfounding parameter based on M₁ and M₂ measured during the cycling. 2.The method of claim 1, wherein the cycling comprises thermal cyclingand/or cycling at varying charge and discharge rates that is performedduring the formation stage of battery where the solid electrolyteinterphase is slowly formed at electrodes of the battery.
 3. The methodof claim 1, wherein determining the compensation factor comprisesdetermining the compensation factor using statistical analysis ofmeasurements obtained during charge/discharge cycling at varying chargeand discharge rates that is performed during the formation stage ofbattery where the solid electrolyte interphase is slowly formed atelectrodes of the battery.
 4. The method of claim 3, further comprisingintroducing controlled temperatures variations during thecharge/discharge cycles.
 5. The method of claim 1, wherein: determiningthe compensation factor comprises measuring M₁ and M₂ during thermalcycling the battery while the battery is at rest and is not beingcharged or discharged; and calculating K as a ratio of M₁ and M₂.
 6. Themethod of claim 1, further comprising: periodically determining K over aperiod of time; and determining a degradation state of the battery basedon a change in K over the period of time.
 7. The method of claim 1,further comprising determining the compensation factor based onstatistical analysis of M₁ and M₂ taken over the multiplecharge/discharge cycles of the battery.
 8. The method of claim 1,further comprising determining the compensation factor based on a ratioof M₁ and M₂ taken over the one or more thermal cycles of the battery.9. The method of claim 1, wherein the parameter of interest is strainand the confounding parameter is temperature or chemical concentration.10. The method of claim 1, further comprising: using the compensationfactor to determine the parameter of interest for the battery; anddetermining a state of health of the battery based on the parameter ofinterest.
 11. The method of claim 10, controlling one or both of thecharge/discharge cycles of the battery and the environment of thebattery based on the state of health of the battery.
 12. The method ofclaim 10, further comprising: periodically determining the compensationfactor the battery over time; and detecting degradation of the batterybased on a change in the compensation factor over time.
 13. The methodof claim 1, wherein the optical sensors are fiber Bragg grating sensors.14. The method of claim 1, wherein the parameter of interest is strain,temperature, chemical composition, vibration, humidity, or accelerationand each confounding parameter is different from the parameter ofinterest and is strain, temperature, chemical composition, vibration,humidity, or acceleration.